Research

Research Interests

My training and primary interests are in Homotopy Theory and (Higher) Category Theory. I became interested in surprising links between Algebraic Topology and Logic, especially Type Theory, which led me to Homotopy Type Theory (HoTT).

My current projects are:

Proving Nicolai's conjecture: Idempotent equivalences are a well behaved notion of weak identity structure.
Developing properties of Δ (fat Delta).
I am also keen to learn about higher semantic models of HoTT, and more generally about higher topoi/categories logic.

WRITINGS

Publications & Preprints

A study of Kock's fat Delta [arXiv] (Submitted)

with Tom de Jong, Nicolai Kraus and Simona Paoli

Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock. We provide a comprehensive study of fat Delta via the theory of monads with arities, and use these results to show that fat Delta is a hypermoment category in the sense of C. Berger. Specifically, by proving that the free relative semicategory monad is strongly cartesian and identifying a dense generator, the theory of monads with arities immediately gives rise to the nerve theorem. We characterise the essential image of the nerve via the Segal condition, and show that fat Delta possesses an active-inert factorisation system. Building on these results, we also establish an isomorphism between two presentations of fat Delta and show that it is a strongly unital and extensional hypermoment category.

Miscellaneous

[Higher Category Theory in Two-Level Type Theory]

First Year's PhD Report.

[Test Categories and the Dendroidal Category] (in French)

Master's thesis, supervised by Clemens Berger.

Talks

[Aberdeen Topology Seminar], A study of Kock's fat Delta.
[YaMCATS 36], [A study of Kock's fat Delta], [slides]
[CL&HC], [A study of Kock's fat Delta], [slides]
[PSSL 109th], [A study of Kock's fat Delta], [slides]
[TYPES 2023], [Categories as semicategories with identities], [slides], [recording].

Page updated

Google Sites

Report abuse